Finding the circumference of a circle is quick and easy. Show  Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher) Follow these easy to follow examples, and you’ll be all set. Let’s jump in! The circumference is the distance around a circle. In other words, it’s the perimeter of the circle. And we find the circumference by using the formula C = 2πr. Circumference of a Circle Formula But what do we do if we only want to find a fraction or a part of the distance around the circle? We need the Arc Length Formula! This means that the length on any arc can be found from its degree measure if the radius of the circle is known. Arc Length of a Circle Formula And as Math Open Reference states, the formula takes the circumference of the entire circle (2πr). It reduces it by the ratio of the degree measure of the arc angle (n) to the degree measure of the entire circle (360). In the video below, you’ll learn how to:
Video – Lesson & Examples45 min
Get access to all the courses and over 450 HD videos with your subscription Monthly and Yearly Plans Available Get My Subscription Now All High School Math ResourcesA circle has radius . What is the circumference, rounded to the nearest tenth? Correct answer: Explanation: Circumference is given by the equation . We can use this equation with the given radius, 4.2, to solve for the circumference. What is the circumference of a circle with a radius of 12? What is the circumference of a circle with a radius of 12? Correct answer: Explanation: To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is We then plug in the number for the radius into the equation yielding We multiply to find the value for the circumference is . The answer is . A circle with an area of 13π in2 is centered at point C. What is the circumference of this circle? Explanation: The formula for the area of a circle is A = πr2. We are given the area, and by substitution we know that 13π = πr2. We divide out the π and are left with 13 = r2. We take the square root of r to find that r = √13. We find the circumference of the circle with the formula C = 2πr. We then plug in our values to find C = 2√13π. A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle? Explanation: First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10. A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?
Possible Answers: 40 ft. 8π + 24 4π + 24 96 ft Explanation: The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π. The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle? Possible Answers: π√5 5π π√2.5 None of the other answers 2.5π Explanation: We first must calculate the distance between these two points. Recall that the distance formula is:√((x2 - x1)2 + (y2 - y1)2) For us, it is therefore: √((4 - 2)2 + (6 - 5)2) = √((2)2 + (1)2) = √(4 + 1) = √5 If d = √5, the circumference of our circle is πd, or π√5. If a circle has an area of , what is the circumference of the circle? Correct answer: Explanation: The formula for the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π. Find the circumference of a circle with a radius of . Possible Answers: Not enough information to solve Correct answer: Explanation: In order to find the circumference, we will use the formula . This figure is a circle with a radius of 3 cm. What is the circumference of the circle (cm)? Correct answer: Explanation: In order to find the circumference of a circle (which is the perimeter or distance around the circle), you must double the radius and multiply by pi (). What is the circumference of a circle with a radius of 4? Correct answer: Explanation: The equation for the circumference of a circle is , so by substituting the given radius into the equation, we get . All High School Math ResourcesWhat is 2πr in circle?Formula for Circumference of a Circle
Circumference is given by the formula C = πd where π = 3.14 and d is the diameter of the circle. Circumference is given by the formula C = 2πr where π = 3.14 and r is the radius of the circle.
Why is the circumference of a circle 2πr?It sounds like you are aware of this, but just to clarify: the formulae 2πr and πd for the circumference of the circle are equivalent because the diameter is twice the radius. The former statement is often more useful simply because the radius of a circle is a property that we often refer to.
|
What is the equation for the circumference of a circle
Related Posts
Copyright © 2024 membukakan Inc.
